Algebra worksheet — GCSE Foundation

1.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

2.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

3.Simplify (5x² + 3x − 2) − (2x² − x + 5)

4.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

5.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

6.Which expression is equivalent to 6x − (2x − 5)?

7.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

8.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

9.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

10.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

11.Write down the expression that means the same as (x + 7) ÷ 4.

12.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

13.Which of these numbers is a cube number?

14.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

15.Write down the gradient of the line with equation y = −x + 3.